Finite temperature field theory and phase transitions

TL;DR

This paper reviews finite temperature field theory, phase transitions, and their applications to baryogenesis, discussing theoretical frameworks, computational techniques, and implications for particle physics models.

Contribution

It provides a comprehensive overview of finite temperature field theory, including renormalization, formalisms, bubble nucleation, and applications to electroweak baryogenesis in the Standard Model and MSSM.

Findings

Equivalence of real and imaginary time formalisms demonstrated.

Conditions for baryogenesis related to Higgs mass bounds established.

Infrared problems and perturbative breakdowns discussed.

Abstract

We review different aspects of field theory at zero and finite temperature, related to the theory of phase transitions. We discuss different renormalization conditions for the effective potential at zero temperature, emphasizing in particular the MS-bar renormalization scheme. Finite temperature field theory is discussed in the real and imaginary time formalisms, showing their equivalence in simple examples. Bubble nucleation by thermal tunneling, and the subsequent development of the phase transition is described in some detail. Some attention is also devoted to the breakdown of the perturbative expansion and the infrared problem in the finite temperature field theory. Finally the application to baryogenesis at the electroweak phase transition is done in the Standard Model and in the Minimal Supersymmetric Standard Model. In all cases we have translated the condition of not washing out any previously generated baryon asymmetry by upper bounds on the Higgs mass.